[tex]5\sqrt{3}=\sqrt{5^2*3}=\sqrt{25*3}=\sqrt{75}\\4\sqrt{5}=\sqrt{4^2*5}=\sqrt{16*5}=\sqrt{80} \\\\75 < 80\; = > \sqrt{75} < \sqrt{80}\; \; = > \; \; 5\sqrt{3} < 4\sqrt{5}[/tex]
[tex]2\sqrt{5}=\sqrt{2^2*5}=\sqrt{4*5}=\sqrt{20}\\3\sqrt{2}=\sqrt{3^2*2}=\sqrt{9*2}=\sqrt{18}\\\\20 > 18\; = > \; \sqrt{20} > \sqrt{18}\; = > \; 2\sqrt{5} > 3\sqrt{2}[/tex]
[tex]2\sqrt{10}=\sqrt{2^2*10}=\sqrt{4*10}=\sqrt{40}\\3\sqrt{5}=\sqrt{3^2*5}=\sqrt{9*5}=\sqrt{45}\\\\40 < 45\; = > \; \sqrt{40} < \sqrt{45}\; = > \; 2\sqrt{10} < 3\sqrt{5}\\\\7\sqrt{2}=\sqrt{7^2*2}=\sqrt{49*2}=\sqrt{98}\\4\sqrt{6}=\sqrt{4^2*6}=\sqrt{16*6}=\sqrt{96}\\\\98 > 96\; = > \; \sqrt{98} > \sqrt{96}\; = > \; 7\sqrt{2} > 4\sqrt{6}[/tex]
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[tex]5\sqrt{3}=\sqrt{5^2*3}=\sqrt{25*3}=\sqrt{75}\\4\sqrt{5}=\sqrt{4^2*5}=\sqrt{16*5}=\sqrt{80} \\\\75 < 80\; = > \sqrt{75} < \sqrt{80}\; \; = > \; \; 5\sqrt{3} < 4\sqrt{5}[/tex]
[tex]2\sqrt{5}=\sqrt{2^2*5}=\sqrt{4*5}=\sqrt{20}\\3\sqrt{2}=\sqrt{3^2*2}=\sqrt{9*2}=\sqrt{18}\\\\20 > 18\; = > \; \sqrt{20} > \sqrt{18}\; = > \; 2\sqrt{5} > 3\sqrt{2}[/tex]
[tex]2\sqrt{10}=\sqrt{2^2*10}=\sqrt{4*10}=\sqrt{40}\\3\sqrt{5}=\sqrt{3^2*5}=\sqrt{9*5}=\sqrt{45}\\\\40 < 45\; = > \; \sqrt{40} < \sqrt{45}\; = > \; 2\sqrt{10} < 3\sqrt{5}\\\\7\sqrt{2}=\sqrt{7^2*2}=\sqrt{49*2}=\sqrt{98}\\4\sqrt{6}=\sqrt{4^2*6}=\sqrt{16*6}=\sqrt{96}\\\\98 > 96\; = > \; \sqrt{98} > \sqrt{96}\; = > \; 7\sqrt{2} > 4\sqrt{6}[/tex]